H∞H∞ control and quadratic stabilization of switched linear systems with linear fractional uncertainties via output feedback

For switched linear systems with linear fractional time-varying uncertainties, the robust HH-infinity control problem is investigated by using linear matrix inequality (LMI) in this paper. First, for a class of unforced switched linear systems, a sufficient condition is derived for stabilization with a prescribed disturbance attenuation level only by switching based on LMI. Then the robust HH-infinity control synthesis via switched output feedback is studied for a switched linear system with linear fractional uncertainties. It is shown that a switched output feedback controller can be designed to stabilize asymptotically the uncertain switched linear systems with an HH-infinity norm bound if a linear matrix inequality condition is feasible under the associated parameters that are selected in advance.